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When I attack with Blitzwing - Relentless Foe and don't flip at least [Orange][Blue]... I don't draw a card, but can I still flip to other mode after the battle?

No, you may not. That is all one ability.
Source: Wizards of the Coast (2019-07-12)    【Link to Ruling】
Tags: Blitzwing, Relentless Foe